Skip to main content

Solid-particle motion in two-dimensional peristaltic flows

  • Tin-Kan Hung (a1) and Thomas D. Brown (a1)

Some insight into the mechanism of solid-particle transport by peristalsis is sought experimentally through a two-dimensional model study (§ 2). The peristaltic wave is characterized by a single bolus sweeping by the particle, resulting in oscillatory motion of the particle. Because of fluid-particle interaction and the significant curvature in the wall wave, the peristaltic flow is highly nonlinear and time dependent.

For a neutrally buoyant particle propelled along the axis of the channel by a single bolus, the net particle displacement can be either positive or negative. The instantaneous force acting upon the particle and the resultant particle trajectory are sensitive to the Reynolds number of the flow (§ 3 and 4). The net forward movement of the particle increases slightly with the particle size but decreases rapidly as the gap width of the bolus increases. The combined dynamic effects of the gap width and Reynolds number on the particle displacement are studied (§ 5). Changes in both the amplitude and the form of the wave have significant effects on particle motion. A decrease in wave amplitude along with an increase in wave speed may lead to a net retrograde particle motion (§ 6). For a non-neutrally buoyant particle, the gravitational effects on particle transport are modelled according to the ratio of the Froude number to the Reynolds number. The interaction of the particle with the wall for this case is also explored (§ 7).

When the centre of the particle is off the longitudinal axis, the particle will undergo rotation as well as translation. Lateral migration of the particle is found to occur in the curvilinear flow region of the bolus, leading to a reduction in the net longitudinal transport (§ 8). The interaction of the curvilinear flow field with the particle is further discussed through comparison of flow patterns around a particle with the corresponding cases without a particle (§ 9).

Hide All
Barton, C. & Raynor, S. 1968 Peristaltic flow in tubes Bull. Math. Biophys. 30, 663680.
Boyarsky, S., Gottschalk, C. W., Tanagho, E. A. & ZIMSKIND, P. D. (eds) 1971 Urodynamics. Academic.
Bungay, P. & Brenner, H. 1973 Pressure drop due to the motion of a sphere near the wall bounding a Poiseuille flow J. Fluid Mech. 60, 8196.
Burns, J. C. & Parkes, T. 1967 Peristaltic motion J. Fluid Mech. 29, 731743.
Fitz-Gerald, J. M. 1972 Mechanics of red-cell motion through very narrow capillaries. Proc. Roy. Soc. B 174, 193227.
Fox, M., Pyrah, L. N. & Raper, F. P. 1965 Management of ureteric stone: a review of 292 cases. Brit. J. Urol. 37, 660670.
Fung, Y. C. 1971 Peristaltic pumping: a bioengineering model. In Urodynamics (ed. S. Boyarsky et al.), pp. 178198. Academic.
Fung, Y. C. & Yih, C. S. 1968 Peristaltic transport J. Appl. Mech. 35, 669675.
Goldsmith, H. L. & Mason, S. G. 1966 In Rheology: Theory and Application (ed. F. R. Eirich), vol. 4, pp. 85-250. Academic.
Happel, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics. Prentice-Hall.
Jaffrin, M. Y. 1971 Inertia and streamline curvature effects on peristaltic pumping Int. J. Engng Sci. 11, 681699.
Jones, A. M. & Knudsen, J. G. 1961 Drag coefficients at low Reynolds numbers for flow past immersed bodies A.I.Ch.E.J. 7, 2025.
Kim, H. L., Labay, P., Boyarsky, S. & Glenn, J. F. 1970 An experimental model of ureteral colic J. Urol. 104, 380391.
Labay, P. C. & Boyarsky, S. 1971 Ureteral peristaltic pressure methods. In Urodynamics, (ed. S. Boyarsky et al.). Academic.
Lew, H. S., Fung, Y. C. & Lowenstein, C. B. 1971 Peristaltic carrying and mixing of chyme in the small intestine J. Biomech. 4, 297315.
Li, C. H. 1970 Peristaltic transport in circular cylindrical tubes J. Biomech. 3, 513523.
Lighthill, M. J. 1968 Pressure-forcing of tightly fitting pellets along fluid-filled elastic tubes J. Fluid Mech. 34, 113143.
Lykoudis, P. S. & Roos, R. 1970 The fluid mechanics of the ureter from a lubrication point of view J. Fluid Mech. 43, 661674.
Rouse, H. & Macagno, E. O. 1966 On the use of models in fluids research. In Hemorheology (ed. A. L. Copley), pp. 231-236. Pergamon.
Shapiro, A. H. 1967 Pumping and retrograde diffusion in peristaltic waves. Proc. Workshop Ureteral Reflux Children, Nat. Acad. Sci., Wash.
Shapiro, A. H., Jaffrin, M. Y. & Weinberg, S. L. 1969 Peristaltic pumping with long wavelengths at low Reynolds number J. Fluid Mech. 37, 799825.
Skalak, R., Chen, P. H. & Chien, S. 1973 Effect of hematocrit and rouleaux on apparent viscosity in capillaries Biorheol. 9, 6787.
Taylor, G. I. 1951 Analysis of the swimming of microscopic organisms. Proc. Roy. Soc. A 209, 447461.
Tong, P. & Vawter, D. 1972 An analysis of peristaltic pumping J. Appl. Mech. 39, 857862.
Wang, H. & Skalak, R. 1970 Viscous flow in a cylindrical tube containing a line of spherical particles J. Fluid Mech. 38, 7596.
Yin, F. C. P. & Fung, Y. C. 1969 Peristaltic waves in circular cylindrical tubes J. Appl. Mech. 36, 5795.
Yin, F. C. P. & Fung, Y. C. 1971 Comparison of theory and experiment in peristaltic transport J. Fluid Mech. 47, 93112.
Zien, T. F. & Ostrach, S. 1970 A long wave approximation to peristaltic motion J. Biomech. 3, 6375.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 13 *
Loading metrics...

Abstract views

Total abstract views: 100 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 25th November 2017. This data will be updated every 24 hours.